Tube-side mass transfer for hollow fibre membrane contactors operated in the low Graetz range - Wang, C. Y.; Mercer, Edwina V.; Kamranvand, Farhad; Williams, Leon; Kolios, Athanasios; Parker, Alison; Tyrrel, Sean; Cartmell, Elise; McAdam, Ewan J. (Elsevier, 2016)
Transformation of the tube-side mass transfer coeﬃcient derived in hollow ﬁbre membrane contactors (HFMC) of diﬀerent characteristic length scales (equivalent diameter and ﬁbre length) has been studied when operated in the low Graetz range (Gz < 10). Within the low Gz range, mass transfer is generally described by the Graetz problem (Sh=3.67) which assumes that the concentration proﬁle comprises a constant shape over the ﬁbre radius. In this study, it is experimentally evidenced that this assumption over predicts mass transfer within the low Graetz range. Furthermore, within the low Gz range (below 2), a proportional relationship between the experimentally determined mass transfer coeﬃcient (Kov) and the Graetz number has been identiﬁed. For Gz numbers below 2, the experimental Sh number approached unity, which suggests that mass transfer is strongly dependent upon diﬀusion. However, within this diﬀusion controlled region of mass transfer, tube-side ﬂuid velocity remained important. For Gz numbers above 2, Sh could be satisfactorily described by extension to the Lévêque solution, which can be ascribed to the constrained growth of the concentration boundary layer adjacent to the ﬁbre wall. Importantly this study demonstrates that whilst mass transfer in the low Graetz range does not explicitly conform to either the Graetz problem or classical Lévêque solution, it is possible to transform the experimentally derived overall mass transfer coeﬃcient (Kov) between characteristic length scales (dh and L). This was corroborated by comparison of the empirical relationship determined in this study (Sh=0.36Gz) with previously published studies operated in the low Gz range. This analysis provides important insight for process design when slow tube-side ﬂows, or low Schmidt numbers (coincident with gases) constrain operation of hollow ﬁbre membrane contactors to the low Gz range.
Keywords: Lumen; Graetz-Lévêque; Graetz problem; Low Reynolds number; Entrance region